If you only have a wire brush, you're at huge disadvantage, but that doesn't mean absolute despair. I have a wire wheel, and have never had to use a brush, but that's how it was done for many years. If you're really going to stick with birds, I would either rig up something with an old fan motor or drill, etc. or buy a wheel, but either way I would have something that spun. It is so easy to let the motor and brush do the work rather than by hand trying to be delicate. So far you've worked on two divers. Alot of fat? Yes!, but a thick skin as well. Wait til you do a puddle duck or worse yet a Teal or Woodie. That's when you'll decide if bird taxidermy is for you! LOL! those birds have a thinner grease (viscosity) than a Diver, but where the grease and fat ends, the skin begins, and it isn't much thicker than toilet paper. I just don't think you can do a real good job fleshing without a wheel, but like I said, I never used just a brush.
Skinning the wings, or inverting as I call it is very easy, and should only take you 30 seconds per wing, once you figure it out. At the arm pit you can pull till you get to your first joint (elbow), without using anything more than a firm tug. The only way you wouldn't be able to do so is if there is a big old BB hole where the armpit or elbow would be. Once you get to the elbow, you can take your thumb and remove the secondaries right away from the bone, popping them off with you thumb as you give it a slight tug. It gets easier with every bird, just make mental notes on the anatomy, not just for the mount, but for the ease of skinning the bird as well.
The odorless mineral spirits is just an easy way to evacuate the water from your skin after the washing and rinsing. You said cool water and dawn dishsoap. You can use warmer than cool water. It will help to remove grease just like doing the dishes. The sudsy water works better at washing away the grease if it is warm rather than cold. Put some Winks or Oxyclean in with you soapy water. I use a small amount of 35% peroxide. It will wash away all the rust and blood, and bring out all the vibrant colors. Like I said before, once you have washed and rinsed the bird real well, you can roll it up in a towel and pat it dry, then you can completely cover the skin in mineral spirits. Shake the skin in the solvent for like five minutes, you'll see water that comes out in the bottom of the mineral spirits. I use an Ice cream pail, and recover the remaining solvent and pour it back in the original container. try to avoid pouring the watery greasy stuff back in the container. You can use a gallon on about twenty ducks easy enough. Where some nice nitrile gloves or some two-ply latex gloves to avoid exposure through the skin.
Any more questions, just give a shout.